ODE
\[ x^2 y''(x)+x y'(x)-y(x)=0 \] ODE Classification
[[_2nd_order, _exact, _linear, _homogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.154005 (sec), leaf count = 16
\[\left \{\left \{y(x)\to \frac {c_1}{x}+c_2 x\right \}\right \}\]
Maple ✓
cpu = 0.013 (sec), leaf count = 13
\[\left [y \left (x \right ) = \frac {\textit {\_C1}}{x}+\textit {\_C2} x\right ]\] Mathematica raw input
DSolve[-y[x] + x*y'[x] + x^2*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> C[1]/x + x*C[2]}}
Maple raw input
dsolve(x^2*diff(diff(y(x),x),x)+x*diff(y(x),x)-y(x) = 0, y(x))
Maple raw output
[y(x) = 1/x*_C1+_C2*x]